Anisotropy Characteristics of Stress Relaxation in Coal: An Improved Fractional Derivative Constitutive Model

Abstract

To study the anisotropy characteristics of coal during stress relaxation, a series of uniaxial compressive stress relaxation experiments are conducted on samples cut perpendicular and parallel to bedding. Some conclusions are as follows: (1) the stress of the specimens undergoes rapid relaxation, transient relaxation and steady relaxation, approximately represented with a negative exponential law, before reaching the final strain. The stress decreases discontinuously at the final strain. (2) Anisotropy is observable from stress relaxation tests. The failure strengths and elastic moduli of the bedding-perpendicular samples are generally greater than those of the bedding-parallel samples due to the hardening effect. At the same strain and before the final strain, the relaxation stress of the bedding-perpendicular samples is also greater than that of the bedding-parallel samples. At the final strain, for the bedding-parallel samples, the relaxation stress increases more evidently with higher initial stress relaxation rate, and the residual stress ratio decrease more remarkably. (3) An improved nonlinear fractional derivative generalized Kelvin model is proposed by replacing the Newton dashpot by the Abel dashpot, and the parameters in the model reflect the sample anisotropy well. This new model is used to fit the stress relaxation data, and the results show an improved accuracy in depicting the nonlinear stress relaxation characteristics of raw lean coal in relation to anisotropy over that of other models.